Field of the Invention
The present invention relates generally to a method and a device for correcting a frequency shift on received symbols.
Description of Related Art
Cyclic prefix or cyclic postfix insertion named also guard interval insertion is well known in telecommunication systems which use for example OFDM (Orthogonal Frequency Division Multiplexing) or SC-OFDM (Single Carrier Orthogonal Frequency-Division Multiplexing) or SC-FDMA (Single Carrier Frequency Division Multiple Access) or SC-FDE (Single Carrier Frequency Domain Equalisation) technologies.
Inserting a cyclic prefix consists in dividing the sample stream in symbols of N samples and inserting at predetermined number Δ of samples at the beginning of each symbol. The Δ samples are a copy of the last Δ samples of the symbol.
Inserting a cyclic postfix consists in dividing the sample stream in symbols of N samples and inserting at predetermined number Δ of samples at the end of each symbol. The Δ samples are a copy of the first Δ samples of the symbol.
Classically, a cyclic prefix is inserted at the beginning of each OFDM or SC-OFDM or SC-FDMA or SC-FDE symbol or a postfix prefix is inserted at the end of each OFDM or SC-OFDM or SC-FDMA or SC-FDE symbol. This is the case for most standards implementing OFDM technology and cyclic prefix like DVB-T (Digital Video Broadcasting-Terrestrial), DVB-T2 (Digital Video Broadcasting-Terrestrial 2), DVB-NGH (Digital Video Broadcasting-Next Generation Handheld), 802.11 family, WiMax, DAB (Digital Audio Broadcasting).
Cyclic prefix or cyclic postfix enables time and frequency synchronisation, reduces or suppresses inter-symbol interference, allows simple equalisation in the frequency domain and enables to measure an instantaneous frequency shift on a symbol basis.
For example, in the paper of J. Van de Beek, Magnus Sandell, Per Ola Börjesson entitled ‘ML Estimation of Time and Frequency Offset in OFDM Systems’, published in IEEE Transactions on Signal Processing’, July 1997, a cyclic prefix can be used to measure an instantaneous frequency shift on a symbol basis.
The estimation is performed in the following way. For each received symbol of size N+Δ, the inner product or the correlation is determined between the first Δ samples and the last Δ samples. In case of a frequency drift fd, when neglecting the noise and for the nth symbol, the result is equal to:
      Γ    n    =                    1        Δ            ⁢                        ∑                      i            =            1                    Δ                ⁢                                  ⁢                              y            i            *                    ⁢                      y                          i              +              N                                            =          ⅇ              j2π        ⁢                                  ⁢                  f          d                ⁢        NT            
where T is the sampling time, yi is the i-th sample and (.)* is the conjugate of (.).
As the phase of the result is proportional to fd, the phase can be estimated directly. For the nth symbol, the phase estimation is denoted as
            f      ^        n    =            1              2        ⁢        π        ⁢                                  ⁢        NT              ⁢          arg      ⁡              (                  Γ          n                )            
where arg(.) is a function which gives the angle of a complex symbol.
It has to be noted here that in case strong echoes exist, it is possible to reduce the related interference by using a number of samples less than Δ for the calculation of Γn.
In order to allow channel estimation and in particular to follow the time variation of the channel, pilots symbols are regularly inserted within symbols.
The time variations may be due to phase noise of the local oscillator of the receiver, to a lack of frequency synchronisation between transmitter and receiver and/or to the displacement speed of the receiver which generate the Doppler frequency shift.
Let us call Ts the symbol length:Ts=(N+Δ)T 
According to the Nyquist theorem, if the pilot symbol insertion rate is
      1          MT      s        ,i.e. a pilot symbol is inserted every M symbol, the bound on the maximum acceptable Doppler shift frequency is:
      B    f    =      1          2      ⁢                          ⁢              MT        s            
For example, this limits the maximum displacement speed at which symbols may be correctly received by the receiver.
Increasing Bf by decreasing M has the drawback to decrease the data throughput.